a)
Since, electric field due to conducting sphere = E = k*q/r^2
where, k = 9*10^9
E = 4.90*10^4 N/C
q = charge on sphere = ??
r = 22.0 cm = 0.22 m
So,
q = (E*r^2)/k
q = (4.90*10^4)*(0.22^2)/(9*10^9)
q = 2.63*10^-7 C
Now , surface charge density() = q/A
where, A = surface area = 4*pi*R^2
here R = radius of sphere = 15.0 cm = 0.15 m
So, A = 4*pi*(0.15^2)
A = 0.282 m^2
So,
= (2.63*10^-7 C)/(0.282 m^2)
= 9.33*10^-7
= 0.933 C/m^2
(b.)
Since Capacitance of conducting sphere(C) = R/k
So,
C = 0.15/(9*10^9)
C = 1.67*10^-11 F
C = 0.167 pF
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